Set a grill to a medium high heat and toast each side of the sourdough slices. Once golden, divide the cheese on top of the slices followed by the ham. Grill for 4-5 minutes further until melted and golden brown, place two of the slice atop the others to complete the sandwich.
Whilst the sandwich toast, heat a splash of oil in a frying pan and fry the eggs until crispy but still with runny yolks, serve on top of the sandwiches.